Theorem jao 498

Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)

Assertion

Ref	Expression
jao	⊢ ((φ → ψ) → ((χ → ψ) → ((φ ∨ χ) → ψ)))

Proof of Theorem jao

Step	Hyp	Ref	Expression
1		pm3.44 497	. 2 ⊢ (((φ → ψ) ∧ (χ → ψ)) → ((φ ∨ χ) → ψ))
2	1	ex 423	1 ⊢ ((φ → ψ) → ((χ → ψ) → ((φ ∨ χ) → ψ)))

Syntax hints:   → wi 4   ∨ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by:  3jao  1243